Boeing has won the order battle at the Paris Air Show after Airbus conceded it cannot catch the U.S. plane maker's tally.

As of Thursday morning, Airbus had won commitments for a total of 326 aircraft, including firm orders for 144 aircraft worth $18.5 billion and Memorandums of Understanding's for 182 aircraft worth $21.2 billion.

Boeing, meanwhile, has a Paris order book of 463 when conversions, previous orders upgraded to newer planes, are stripped out.

"Is this a slower show than previous years? Yes it is. Are we conceding that Boeing sold a few more airplanes than we did? Yes," said Airbus COO of Commercial Customers, John Leahy in comments reported by Reuters, Thursday.

Much of Boeing's Paris success has come in the form of the launch of their 737 MAX 10 airplane. The single-aisle plane can carry up to 230 passengers and competes with the Airbus A320neo family.

Boeing says it is increasing production of its 737 range from 42 to 47 planes a month by the end of 2017 and will reach 57 a month by 2020 to meet demand.

Airbus's Leahy claimed Boeing's MAX 10 launch was not as impressive as it appeared, benefiting from a high number of airlines and leasing companies shifting orders to the new plane.

Leahy retirement

The outspoken sales chief for Airbus has also confirmed he will retire at some point this year.

ERIC PIERMONT/AFP/Getty Images

Airbus Chief Operating Officer John Leahy

The New York-born businessman joined Airbus North America in January 1985, becoming head of sales soon after.

Leahy is credited with leading the massive expansion in Airbus's market share from 1993 onwards.